21/4x+0.5x=44

Solution for 21/4x+0.5x=44 equation:

21/4x+0.5x=44

We move all terms to the left:

21/4x+0.5x-(44)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

0.5x+21/4x-44=0

We multiply all the terms by the denominator


(0.5x)*4x-44*4x+21=0

We add all the numbers together, and all the variables

(+0.5x)*4x-44*4x+21=0

We multiply parentheses

0x^2-44*4x+21=0

Wy multiply elements

0x^2-176x+21=0

We add all the numbers together, and all the variables

x^2-176x+21=0

a = 1; b = -176; c = +21;
Δ = b2-4ac
Δ = -1762-4·1·21
Δ = 30892
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{30892}=\sqrt{4*7723}=\sqrt{4}*\sqrt{7723}=2\sqrt{7723}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-2\sqrt{7723}}{2*1}=\frac{176-2\sqrt{7723}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+2\sqrt{7723}}{2*1}=\frac{176+2\sqrt{7723}}{2}
$